Stability and absorbing set of parabolic chemotaxis model of Escherichia coli
This paper is devoted to model (1) for escherichia coli, introduced in [1]. Based on the experimental observations of Budrene and Berg [2, 3], Tyson and coworkers derived (1) with n cell density, c chemotrattactant concentration and s stimulant concentration. Our aim is to study the stability of co...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Vilnius University Press
2013-04-01
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| Series: | Nonlinear Analysis |
| Subjects: | |
| Online Access: | http://www.journals.vu.lt/nonlinear-analysis/article/view/14023 |
| Summary: | This paper is devoted to model (1) for escherichia coli, introduced in [1]. Based on the experimental observations of Budrene and Berg [2, 3], Tyson and coworkers derived (1) with n cell density, c chemotrattactant concentration and s stimulant concentration. Our aim is to study the stability of constant meaning full solution and ultimately boundedness of the solutions. Precisely:
(i) linear and nonlinear stability is proved by using a peculiar Lyapunov function,
(ii) the ultimately boundedness of the solutions in the L2-norm is obtained,
(iii) conditions guaranteeing the global stability are also obtained.
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| ISSN: | 1392-5113 2335-8963 |